Negative Numbers and the Full Number Line

Hey! I'm Lumi, and today we're going to stretch the number line in a direction you might not have explored before — below zero. You already know numbers like 1, 2, 3, and so on. But what happens when temperature drops below freezing? Or when you owe someone money? We need numbers that go the other way. That's where negative numbers come in. Every positive number has an opposite called its negative. The opposite of 3 is -3 (read: "negative three"). The opposite of 10 is -10. And every negative number has a positive opposite, too — the opposite of -3 is 3, and the opposite of -10 is 10. Zero is special — it's its own opposite, right in the middle. On a number line, positive numbers sit to the RIGHT of zero, and negative numbers sit to the LEFT. The further left you go, the smaller the number. So -5 is less than -1, even though 5 looks bigger than 1. That trips a lot of people up! Here's a trick: picture a thermometer lying on its side. Warmer temperatures are to the right, colder ones to the left. -8°C is colder (further left) than -2°C, so -8 < -2. Whenever you're not sure which integer is greater, just find both on the number line. The one further to the right is always the greater value. And when placing a number on the line, count the steps from zero — negative numbers step to the left, positive numbers step to the right. If you ever need to check your work and there's no number line in front of you, draw your own! Put a dot in the middle for zero, add tick marks evenly on both sides, label them 1, 2, 3... to the right and -1, -2, -3... to the left, then count the steps to place any integer exactly where it belongs.